1 Introduction

Since the beginning of the COVID-19 epidemic, policy makers in different countries have introduced different political action to contrast the contagion. The containment restrictions span from worldwide curfews, stay-at-home orders, shelter-in-place orders, shutdowns/lockdowns to softer measures and stay-at-home recommendations and including in addition the development of contact tracing strategies and specific testing policies. The pandemic has resulted in the largest amount of shutdowns/lockdowns worldwide at the same time in history.

The timing of the different interventions with respect to the spread of the contagion both at a global and intra-national level has been very different from country to country. This, in combination with demographical, economic, health-care related and area-specific factors, have resulted in different contagion patterns across the world.

Therefore, our goal is two-fold. The aim is to measure the effect of the different political actions by analysing and comparing types of actions from a global perspective and, at the same time, to benchmark the effect of the same action in an heterogeneous framework such as the Italian regional context.

In doing so, some issue arises concerning the identification and codification of the different measures undertaken by governments, the analysis related to whether a strategies resemblance can be detected across countries and the measurement of the effects of containment policies on contagion. Thus, after an introductory section explaining data and variables, a second section regards some explanatory analysis facing the codification of containment policies and the strategies resembling patterns. The third section deals with the measurement of policies effect from a global perspective, lastly the forth section analyze Italian lockdown and regional outcomes. Conclusion are drawn in the last section.

2 Data and Variables

The data repositories used for this project are COVID-19 Data Repository by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University1 for contagion data (Dong, Du, and Gardner (2020)), and Oxford COVID-19 Government Response Tracker (OxCGRT)2 for policies tracking (Thomas et al. (2020)), together with World Bank Open Data Repository for demographic data.

As regards contagion data, we used as main variable the active cases, defined as the total confirmed cases (cumulative confirmed positive cases including presumptive positive) minus total deaths minus total recovered. For further information see Thomas et al. (2020).

As regards policies variables, the Oxford COVID-19 Government Response Tracker (OxCGRT) collects all the containment policies adopted by government worldwide by making available information on 11 indicators of government containment responses of ordinal type. These indicators measure policies on a simple scale of severity / intensity and are reported for each day a policy is in place, specifying if they are “targeted”, applying only to a sub-region of a jurisdiction, or a specific sector; or “general”, applying throughout that jurisdiction or across the economy.

The containment ordinal variables considered are:

Name Measurement Description Category
School closing Ordinal Closings of schools and universities 0- No measures 1 - recommend closing 2 - Require closing (only some levels or categories, eg just high school, or just public schools) 3 - Require closing all levels
Workplace closing Ordinal Closings of workplaces 0- No measures 1 - recommend closing (or work from home) 2 - require closing (or work from home) for some sectors or categories of workers 3 - require closing (or work from home) all-but-essential workplaces (e.g. grocery stores, doctors)
Cancel public events Ordinal Cancelling public events 0- No measures 1 - Recommend cancelling 2 - Require cancelling
Restrictions on gatherings Ordinal Cut-off size for bans on private gatherings 0 - No restrictions 1 - Restrictions on very large gatherings (the limit is above 1000 people) 2 - Restrictions on gatherings between 101-1000 people 3 - Restrictions on gatherings between 11-100 people 4 - Restrictions on gatherings of 10 people or less
Close public transport Ordinal Closing of public transport 0 - No measures 1 - Recommend closing (or significantly reduce volume/route/means of transport available) 2 - Require closing (or prohibit most citizens from using it)
Stay at home requirements Ordinal Orders to shelter-in-place and otherwise confine to home 0 - No measures 1 - recommend not leaving house 2 - require not leaving house with exceptions for daily exercise, grocery shopping, and ‘essential’ trips 3 - Require not leaving house with minimal exceptions (e.g. allowed to leave only once a week, or only one person can leave at a time, etc.)
Restrictions on internal movements Ordinal Restrictions on internal movement 0 - No measures 1 - Recommend not to travel between regions/cities 2 - internal movement restrictions in place
International travel controls Ordinal Restrictions on international travel 0 - No measures 1 - Screening 2 - Quarantine arrivals from high-risk regions 3 - Ban on arrivals from some regions 4 - Ban on all regions or total border closure
Public info campaigns Ordinal Presence of public info campaigns 0 -No COVID-19 public information campaign 1 - public officials urging caution about COVID-19 2 - coordinated public information campaign (e.g. across traditional and social media)
Testing policy Ordinal Who can get tested by public health system 0 - No testing policy 1 - Only those who both (a) have symptoms AND (b) meet specific criteria (e.g. key workers, admitted to hospital, came into contact with a known case, returned from overseas) 2 - testing of anyone showing COVID-19 symptoms 3 - open public testing (e.g. drive through testing available to asymptomatic people)
Contact Tracing Policy Ordinal Are governments doing contact tracing? 0 - No contact tracing 1 - Limited contact tracing - not done for all cases 2 - Comprehensive contact tracing - done for all identified cases

Lastly, a set of confounders variables has been considered in the analysis. These can be divided into three main areas:

  1. Longitudinal economic variables from Thomas et al. (2020);

  2. Longitudinal health system variables from Thomas et al. (2020);

  3. Fixed demographic/economic/health variables from the World Bank Open Data.

2.1 Longitudinal economic Variables

We analyze four economic variables from Thomas et al. (2020):

Name Measurement Description Category
Income Support Ordinal Government income support to people that lose their jobs 0 - no income support; 1 - government is replacing less than 50% of lost salary, 2 - government is replacing more than 50% of lost salary
Debt/contract relief for households Ordinal Government policies imposed to freeze financial obligations 0 - No; 1 - Narrow relief, specific to one kind of contract; 2 - broad debt/contract relief
Fiscal measures USD Economic fiscal stimuli
International support USD monetary value spending to other countries

However, having \(9\) ordinal policies lockdown covariates, the two first economic variables are combined into one continuous variable using the Polychoric Principal Component Analysis, to diminish the number of covariates inside the model.

The Economic PCA has a temporal pattern, with more considerable variability near the last days of observations. Korea and Singapore’s population received less money from the government than the other countries. The European ones are the best as financial support to society.

Therefore, the USD’s two economic variables are examined and transformed into a logarithmic scale to de-emphasize large values.

The fiscal measure and international support variables have a large within-clusters variability. As we will see, these two variables will not enter into the final model.

For further details about the definition of the economic variables, please see the BSG Working Paper Series.

2.2 Demographic/economic/health system fixed variables

We analyze \(8\) variables from the World Bank Open Data that are fixed along the temporal dimension:

Name Measurement
Population Numeric
Population ages 65 and above (% of total population) Numeric
Population density (people per sq. km of land area) Numeric
Hospital beds (per 1,000 people) Numeric
Death rate, crude (per 1,000 people) Numeric
GDP growth (annual %) Numeric
Urban population (% of total population) Numeric
Surface area (sq. km) Numeric

Korea and Singapore seem to be the two youngest countries; it could be a reason for their low number of active people during the pandemic period.

The population density of the first Cluster seems weird, it is due by the Singapore situation. Probably, the number of hospital beds are directly associated.

Another time the Singapore situation is clear analyzing the first Cluster. We have a large density population, so lower surface area than the ones of the other countries.

2.3 Longitudinal health system variables

We analyze \(2\) health systems’ variables from Thomas et al. (2020):

Name Measurement Description
Emergency Investment in healthcare USD Short-term spending on, e.g, hospitals, masks, etc
Investment in vaccines USD Announced public spending on vaccine development

The set of the health systems’ variables are transformed into one continuous variable using the Polychoric Principal Component Analysis, in order to reduce the number of covariates in the model.

3 Containment strategies and resembling patterns

Identification and codification of different measures undertaken by governments performed by University of Oxford results in 11 ordinal variables selected as lockdown policies. This sets up the necessity to analyze and to aggregate them in a synthetic way in order to find out whether specific combinations of those policies making up political strategies come out to have a resemblance pattern across countries.

Therefore, we performed a Principal Component Analysis based on the polychoric correlation. It allows to estimate the correlation between two theorised normally distributed continuous latent variables, from two observed ordinal variables. It has no closed form but it is estimated via MLE assuming the two latent variables follows a bivariate normal density.

The interpretation of the first three principal components (accounting for the 80% of total variance) appears to be clear (see Figure ): the first one is closely related with freedom of movements and gathering restrictions together with information campaigns strategy, crucial in cases of draconian measures, the second one is related with the strategy of informing and testing the population, lastly the third one is related to informing and contact tracing the population. Summarizing, on one hand a first containment strategy aims at social distancing the entire population, on the other hand a second one aims at act locally and rapidly detect and isolate the positive cases, with two (alternative or complementary) tools: tracing contacts of infected and/or blanket population testing.

\label{fig:figs}First 3 Principal Components Loadings.

First 3 Principal Components Loadings.

We want now to figure out which countries have adopted the undelined strategies and whether there is a strategies resemblance across countries, considering both the combination of measures undetaken and the timing w.r.t. the day of the first contagion detection on country soil. In order to do so, we performed a functional co-clustering of the first three principal components taking into account 20 countries in a specific time span (which varies from country to country) that depends on when the first covid cases has been detected on national soil. We perfomed an alignment of the contagion pattern from the 10th day before first contagion detection, in order to include also relevant information on the prevention measures.

Considering a matrix of 20 countries (rows) of 3 curves (columns or functional features- restriction-based, testing-based and tracing-based policies) s.t. \(x=(x_{ij}(t))_{1\leq i \leq 20; 1 \leq j\leq3}\) with \(t \in [0,85]\), we reconstructed the functional form of the data from their discrete observations (85 days) by assuming that curves belong to a finite dimensional space spanned by a basis of functions and then we estimated a functional latent block model used for co-clustering with the funFEM R package developed by Bouveyron and Jacques (2015).

The two policies clusters depicts Restriction-based policies on one hand, Tracing and Testing-based policies on the other hand, confirming that these last two policies reflects a common strategy as described above.

The countries clusters are displayed in Figure : (South Korea, Singapore), (Germany, Sweden), (USA, Canada, Greece, Portugal), (Italy, Spain, Ireland, UK, Netherlands), (Norway, Denmark, Finland, France, Belgium, Switzerland, Austria). The interpretation can be grasped in Figure . South Korea and Singapore political strategy is characterized by the detection and isolation of the positive cases via contact tracing and mild testing policies, without any relevant social distancing action. On the contrary Germany, Sweden strategy was to detect and isolate positive cases via an extensive testing policy strategy, without any strong social distancing measures in order to protect the economy. A very different strategy has been adopted by the cluster including Italy, Spain, Ireland, UK and Netherlands, which acted with social distancing measures at different temporal stages (considering in particular the north european countries of the cluster) but promptly with respect to the first contagion inside national borders. In particular the strategies of Ireland, UK and Netherland was very strict concerning school and workplace closing as well as gathering and international movement restiction, weaker as regards stay at home recommendations, internal movement restriction and transport closing but at the same time relying on a strong information campaign. On the other hand, Italy and Spain sharpened up stay at home and internal movement restrictions. USA, Canada, Greece and Portugal has adopted intermittently social distancing measures in addition with strong social tracing during the second part of the considered period. Lastly, Norway, Denmark, Finland, France, Belgium, Switzerland, Austria has adopted intermediate social distancing measure, in line with other European countries, but without any relevant testing or tracing measure in addition.

\label{fig:figs3}Clusters average functionals related to Social Distancing Restrinction, Testing and Tracing policies aligned at the day of the first contagion (vertical blue line).

Clusters average functionals related to Social Distancing Restrinction, Testing and Tracing policies aligned at the day of the first contagion (vertical blue line).

4 Effect of policies from a global perspective

In order to analyze which countries adopt the “optimal” policy measures to contain the contagion of COVID-19, we restrict the full range of responses to COVID-19 from governments around the countries analyzed in Section 3, i.e., Korea, Singapore, Germany, Canada, Sweden, Greece, Portugal, Spain, United States of America, Irland, United Kingdom, Italy, Netherlands, Austria, Switzerland, Finland, Norway, Denmark, and France.

The daily number of active persons is analyzed as a measure of the COVID-19 situation, i.e., the number of confirmed minus the number of deaths minus the number of recovered. Being a count variable, we decide to use a Negative Binomial Regression, also correcting for the possible overdispersion. Therefore, the hierarchical structure is induced by the nested structure of countries inside the clusters and by the longitudinal structure. For that, we decide to use a generalized mixed model with family negative binomial. The countries, clusters, and date’s information are supposed to be used as random effects in the model. The indicators from Thomas et al. (2020) and the demographic/economic/health variables from the World Bank Open Data enter as fixed effect in the model.

So, the aim is to understand how the lockdown policies influence the number of active people. The observations are aligned concerning the first active case across the countries to have observations directly comparable from a longitudinal point of view. The following Figure represents the number of active people during \(131\) days for each countries, and the corresponding mean value of the clusters.

The temporal variability between countries and clusters is clear, as confirmation about the decision to use the generalized mixed model.

4.1 Model

The aim is to model the number of active people, i.e., confirmed - deaths - recovered, after \(14\) days, when the lockdown policies were applied. Therefore, the number of active people lagged to \(t+14\) days, and an offset term representing the number of active people at time \(t\) are considered to analyze the influences of the restrictions imposed at time \(t\) on the number of active at time \(t+14\).

The data has a three-level structure. The variability of the data comes from nested sources: countries are nested within clusters, and the observations are repeated across time, i.e., longitudinal data.

For that, the mixed model approach is considered to exploit the different types of variability coming from the hierarchical data structure. At first, the Intraclass Correlation Coefficient (ICC) is computed:

\[ ICC_{date; active} = 0.0936 \quad ICC_{Countries; Active} = 0.4015 \quad ICC_{Clusters; Active} = 0.0951 \]

Therefore, the \(40.15\%\) of the data’s variance is given by the random effect of the countries, while the \(9.36\%\) by the temporal effect and \(9.51\%\) by the clusters effect. Therefore, the mixed model requires a random effect for the countries; the other two effects is selected using the conditional AIC.

The dependent variable is the number of active persons; therefore, a count data model is considered. To control the overdispersion of our data, the negative binomial regression with Gaussian-distributed random effects is performed using the glmmTMB R package developed by Brooks et al. (n.d.). Let \(n\) countries, and country \(i\) is measured at \(n_i\) time points \(t_{ij}\). The active person \(y_{ij}\) count at time \(t+14\), where \(i=1,\dots, n\) and \(j = 1, \dots,n_i\), follows the negative binomial distribution:

\[y_{ij} \sim NB(y_{ij}|\mu_{ij}, \theta) = \dfrac{\Gamma(y_{ij}+ \theta)}{\Gamma(\theta) y_{ij}!} \cdot \Big(\dfrac{\theta}{\mu_{ij} + \theta}\Big)^{\theta}\cdot \Big(\dfrac{\mu_{ij}}{\mu_{ij} + \theta}\Big)^{y_{ij}}\] where \(\theta\) is the dispersion parameter that controls the amount of overdispersion, and \(\mu_{ij}\) are the means. The means \(\mu_{ij}\) are related to the other variables via the logarithm link function:

\[\log(\mu_{ij}) = \log(T_{ij}) + X_{ij} \beta + Z_{ij} b_i \quad b_i \sim \mathcal{N}(0,\psi)\]

where \(\log(T_{ij})\) is the offset that corrects for the variation of the count of the active person at time \(t\), and \(\text{E}(y_{ij}) = \mu_{ij}\), \(\text{Var}(y_{ij}) = \mu_{ij} (1 + \mu_{ij}\theta)\) from Hardin and Hilbe (2018). The \(X_{ij}\) is the design matrix for the fixed effects, i.e., economic, demographic and health variables (the confounders described in section 2), and \(\beta\) the corresponding set of fixed parameters. In the same way, \(Z_{ij}\) is the design matrix describing the random effect regarding the countries and the date, and \(b_i\) the corresponding parameter.

After some covariates selection steps and random effects selection, the final model returns these estimations for the fixed effects:

Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.012 0.326 -0.035 0.972
pca_EC -0.547 0.070 -7.791 0.000
pop_density_log 0.103 0.031 3.354 0.001
pca_hs 0.053 0.020 2.607 0.009
workplace_closingF1 -0.290 0.138 -2.108 0.035
workplace_closingF2 -1.191 0.134 -8.902 0.000
workplace_closingF3 -0.513 0.170 -3.021 0.003
gatherings_restrictionsF1 -0.506 0.162 -3.120 0.002
gatherings_restrictionsF2 -1.259 0.141 -8.945 0.000
gatherings_restrictionsF3 -1.519 0.173 -8.804 0.000
gatherings_restrictionsF4 -1.702 0.179 -9.513 0.000
transport_closingF1 -0.056 0.106 -0.527 0.598
transport_closingF2 -0.501 0.198 -2.529 0.011
stay_home_restrictionsF1 -0.057 0.109 -0.528 0.598
stay_home_restrictionsF2 -0.111 0.148 -0.751 0.453
stay_home_restrictionsF3 -0.824 0.292 -2.826 0.005
testing_policyF1 0.216 0.091 2.376 0.017
testing_policyF2 0.558 0.113 4.945 0.000
testing_policyF3 1.349 0.158 8.544 0.000
contact_tracingF1 0.196 0.083 2.369 0.018
contact_tracingF2 0.360 0.095 3.784 0.000
ClustersCl2 1.461 0.173 8.454 0.000
ClustersCl3 1.955 0.158 12.377 0.000
ClustersCl4 2.365 0.148 16.029 0.000
ClustersCl5 2.403 0.159 15.122 0.000

while the variance for the random effects are equals:

Variance
Country 0.283
Date 4.320

We drop off the random effect associated with the Clusters having low variability, and the conditional AIC equals the one computed without the variable Clusters as a random intercept.

The marginal \(R^2\), i.e., the variance explained by the fixed effects, equals \(0.28\), while the conditional one, i.e., the variance explained by the entire model, including both fixed and random effects, equals \(0.89\) considering the lognormal approximation Nakagawa and Schielzeth (2013).

Therefore, the model seems correctly formulated. We will analyze the effects related to the following variables:

  1. The fixed effect of the lockdown policies;

  2. The fixed effect of the clusters;

  3. The fixed effect of the combination of lockdown policies and clusters;

  4. The random effect of the countries;

4.1.1 LOCKDOWN POLICIES

In the following plot, we can see the effect of lockdown policies on predicted actives after 14 days.

We can note that in general, the strong lockdown policies work with respect to impose no measure. For example, if the government prohibits most citizens from using it, the number of active people diminishes around \(39.4\%\) with respect to imposing no public transport measures. Also, we can note that weak gatherings restrictions still work concerning impose no action. For example, restrictions on gatherings between 100-1000 people diminish the number of active persons around \(71.62\%\). However, we can see a reverse situation analyzing the effects regarding the variables describing the testing and tracing policies. Probably, strong testing and tracing policies lead to discovering more infected people.

The following plot represents the effects of two policies, i.e., workplace closing and gatherings restriction, on predicted active people \(14\) days after applying these policies.

The combination of gatherings restrictions and workplace closing works, the number of actives decreases, also if the weak limit on reunion is applied.

In the same way, the following plot represents the effects of the combination of tracing and testing policies.

These two policies lead to an increase in the number of active people recorded.

4.1.2 CLUSTERS

The following plot represents the effects of the clusters on predicted actives after \(14\) respect to the cluster associated with Italy.

We can see that Korea and Singapore are the best countries that acted appropriately, while Sweden, Germany, Portugal, and Greece are better than the other European countries. Finally, the USA and Canada are better than the other European countries except for Sweden and Germany. The following multiple comparison procedure adjsted by Tukey’s pvalues adjustment.

Std Test Pvalues
Cl2 - Cl1 0.1728607 8.4537148 0.0000000
Cl3 - Cl1 0.1579392 12.3769088 0.0000000
Cl4 - Cl1 0.1475377 16.0285639 0.0000000
Cl5 - Cl1 0.1589185 15.1220280 0.0000000
Cl3 - Cl2 0.1368272 3.6066195 0.0026450
Cl4 - Cl2 0.1247493 7.2425455 0.0000000
Cl5 - Cl2 0.1238172 7.6068183 0.0000000
Cl4 - Cl3 0.1059615 3.8695069 0.0009203
Cl5 - Cl3 0.0843556 5.3152569 0.0000007
Cl5 - Cl4 0.0903481 0.4245005 0.9926520

4.1.3 INTERACTION LOCKDOWN POLICIES AND CLUSTERS

In this Section, the effects of the interaction between each significant lockdown policy and clusters are examined.

4.1.3.1 Testing policies

4.1.3.2 Contact Tracing

4.1.3.3 Gatherings Restrictions

4.1.3.4 Stay Home Restrictions

4.1.3.5 Workplace Closing

4.1.3.6 Transport Closing

4.1.4 COUNTRIES

In this Section, the countries’ effects on the number of active people are analyzed, considering \(4\) type of scenarios:

  1. No measures of lockdown, tracing and testing policies;

  2. Maximum restriction of lockdown, tracing and testing policies;

  3. Only maximum level of contact tracing and testing policies;

  4. Only maximum restriction of lockdown/social distancing policies.

The effects are computed considering \(100\) and \(1000\) active people at time \(t\), when the policies are applied. The other covariates are fixed and equal to the mean value.

If the government doesn’t impose any measure to contrast the coronavirus, the number of active people after \(14\) days will increase, in particular in the fourth cluster, i.e., Spain, Italy, Irland, United Kingdom, and the Netherlands. The situation gets worst if the number of active people at time \(t\) is large.

The situation gets better if the government applied the strong level of restrictions about social distancing and the strong levels of testing and tracing policies. However, the increasing of the number of active people due to testing and tracing policies influences the analysis of the effects, as you can see in the following plot:

The best situation, as expected is the follows:

i.e., the governements apply the strong levels of all lockdown policies, in this case the testing and tracing variables are imposed to \(0\).

4.2 To sum up

  1. Lockdown policies work with respect to impose no measure in general;

  2. Weak gatherings restrictions still work, i.e., restrictions on gatherings between 100-1000 people;

  3. Strong Testing and Tracing policies lead to discovering more infected people;

  4. Korea and Singapore are the best countries that acted properly;

  5. Sweden, Germany, Portugal, and Greece better than the other UE countries;

  6. The USA, and Canada better than the other UE countries except for Sweden and Germany.

5 Italian lockdown and regional outcomes

6 Supplementary materials

All the codes used for this analysis are available on Github. The report was written by rmarkdown, fully reproducible. You can find the rmarkdown file in Github.

References

Bouveyron, Charles, and Julien Jacques. 2015. “FunFEM: An R Package for Functional Data Clustering.” In Quatrième Rencontres R.

Brooks, M. E., K. Kristensen, K. J. van Benthem, A. Magnusson, C. W. Berg, A. Nielsen, H. J. Skaug, M. Mächler, and B. Bolker. n.d. “GlmmTMB Balances Speed and Flexibility Among Packages for Zero-Inflated Generalized Linear Mixed Modeling.” The R Journal 9 (2): 378–400.

Dong, E., H. Du, and L. Gardner. 2020. “An Interactive Web-Based Dashboard to Track Covid-19 in Real Time.” Lancet Infect Dis.

Hardin, J. W., and J. M. Hilbe. 2018. Generalized Linear Models and Extensions. 4th ed. Stata Press.

Nakagawa, S., and H. Schielzeth. 2013. “A General and Simple Method for Obtaining \(R^2\) from Generalized Linear Mixed‐effects Models.” Methods in Ecology and Evolution 4 (2): 133–42.

Thomas, H., S. Webster, A. Petherick, T. Phillips, and B. Kira. 2020. “Oxford Covid-19 Government Response Tracker, Blavatnik School of Government.” Data Use Policy: Creative Commons Attribution CC BY Standard.

  1. https://github.com/CSSEGISandData/COVID-19/tree/master/csse_covid_19_data↩

  2. https://github.com/OxCGRT/covid-policy-tracker↩